This paper is aimed at proposing an efficient proxy blind signcryption scheme that provably satisfy the security properties of both proxy and blind signatures, based on the hardness assumptions of the ECDLP and the permutation shifting problem.
Subsequently, we sketch some previous works of the same type with corresponding a proxy blind signature technique based on ECDLP from their respective backgrounds, which will be compared to our proposed scheme in Section 4 and 5.
We now sketch the technique due to Brown and Gallant  for solving ECDLP instances P, [alpha]P, [[alpha].
In the extreme case where there is a factor d | (p - 1) with d [approximately equal to] [square root of (p)], then one can solve the ECDLP in O([?
ECDLP](t) denote the number of Hash queries, the range space of the one-way hash function, the number of Send queries, the size of D, and the advantage of in breaking the ECDLP, respectively.
In addition, since the values V and W are based on the difficulty of ECDLP, it is impossible to compute the random numbers [N.
Similarly breaking ECDLP
is also computationally impractical since it is based on Discrete Logrithmic Problem.
While, for attacker it would be a hard problem to access corresponding secret parameters, nearly equivalent to solving the ECDLP
S]G, the adversary will face the ECDLP to derive [x.
Hence, the confidentiality of the session key is protected under the ECDLP or OWHF assumption.
Due to the ECDLP
computational problem, he cannot get [PB.
Our protocol is semantically secure against a chosen ciphertext attack if there is no polynomial-time algorithm that solves the ECDLP
with non-negligible probability.